We will show that gauge theory can be described by an almost product structure, which is a certain type of endomorphism of the tangent bundle. We will recover the gauge field strength as the Nijenhuis tensor of this endomorphism. We discuss a generalization to the case of a general Kaluza-Klein theory. Furthermore, we will look at the classification of these almost product structures in the cas...

This article introduces the problem of finding intrinsic torsion varieties associated to G -structures on a fixed parallelizable Riemannian manifold. As an illustration, the intrinsic torsion varieties of orthogonal almost product structures are analysed on the Iwasawa manifold.